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Deformation/rigidity theoryと冨田・竹崎理論

变形/刚性理论和富田竹崎理论

基本信息

批准号：
20K14324
负责人：
磯野優介
金额：
$ 2.66万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Early-Career Scientists
财政年份：
2020
资助国家：
日本
起止时间：
2020-04-01 至 2024-03-31
项目状态：
已结题

项目摘要

フォンノイマン環とは，（簡単に言えば）無限次元の行列環の事である．特にトレース写像を持たない場合に，III型フォンノイマン環という．これは物理学にも現れる自然な研究対象であり，私はこれを数学的な視点から研究している．本研究は，トレース写像を持つ場合に得られた近年の研究結果を，III型の場合に再現する事を基本的目標としている．特に冨田竹崎理論の重要な道具である連続核を用いた研究を行う．今年度も，前年度に引き続きHaagerup-Stormer予想(1991)に取り組んだ．これはIII型フォンノイマン環の自己同型に関する予想であり，非常にいい加減に説明すると以下のようなものである：環上の状態（良い線形汎関数の事）の性質をあまり変えない自己同型はモジュラー作用素しかない．従順環（物理学に現れるクラス）については成り立つ事が知られており，非従順環の場合に成り立つ例は，私とC. Houdayer氏の共同研究によって前年度に得られていた．ただし前年度に得られた例は全て，almost periodicと呼ばれるクラスに入っていた．今年度はこのalmost periodicという仮定をはずした例を探した．結果として，前年度の研究で得た主定理の一つを一般化する事に成功した．これを用いてalmost periodicでない場合の例が得られるはずであるが，これはまだ現在も研究中である．これらの証明では上述した近年の研究結果の一つである「二つの状態に対するintertwiningの技術」が本質的な役割を果たしている．

This study focuses on the study of the nature of the environment, the study of physics, the study of the nature of nature, the study of mathematics, the study of mathematics, and the study of mathematics. According to the research results of recent years, the basic purpose of the study was rediscovered. Takesaki Takesaki Theory of Takesaki, Takesaki, Takeshi, Takesaki, Takasaki, Takesaki, Tak In the previous year, I would like to (1991) collect the information of the organization. The environment of the same type of Haagerup-Stormer would like to have the same kind of information. It is very important to know that the following information is required: the following information: the following is the most important thing: the following is the best way to know that you are the same type of person. Private C. Houdayer's joint study of the previous year received a full list of cases in the previous year, and almost periodic called for a review of the previous year. This year, we have received a review of the general situation in the previous year. This year, we have made a survey of the general situation in the previous year. The previous year's study concluded that the results of the previous year's study concluded that the results of the previous year's study were successful. The results of the previous year's study showed that the results of the previous year's study showed that the results of the previous year's study concluded that the results of the previous year's study had been concluded that the results of the previous year's study had been concluded that the results of the previous year's study had been concluded that the results of the previous year's study had been concluded that the results of the previous year's study had been concluded that the results of the previous year's study had been successful. The results of the previous year's study had been concluded that the results of the previous year's study had been concluded that the results of the previous year's study had been successful.